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Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks

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  • Liu, Linna
  • Zhu, Quanxin

Abstract

Stability of numerical solutions to stochastic delay differential equations have received an increasing attention, but there has been so far little work on the stability analysis of numerical solutions to stochastic delay Hopfield neural networks. The aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks by using two approaches: the Euler method and the backward Euler method. Under some reasonable conditions, both the Euler scheme and the backward Euler scheme are proved to be almost sure exponential stability. In particular, the Euler method and the backward Euler method are mainly based on the semimartingale convergence theorem.

Suggested Citation

  • Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:698-712
    DOI: 10.1016/j.amc.2015.05.134
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    References listed on IDEAS

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    1. Zhao, Guihua & Song, Minghui & Yang, Zhanwen, 2015. "Mean-square stability of analytic solution and Euler–Maruyama method for impulsive stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 527-538.
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    Cited by:

    1. Nie, Rencan & Cao, Jinde & Zhou, Dongming & Qian, Wenhua, 2019. "Analysis of pulse period for passive neuron in pulse coupled neural network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 277-289.
    2. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    3. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    4. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    5. Zhifu Jia & Cunlin Li, 2023. "Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    6. Tan, Jianguo & Tan, Yahua & Guo, Yongfeng & Feng, Jianfeng, 2020. "Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Wan, Li & Zhou, Qinghua & Liu, Jie, 2017. "Delay-dependent attractor analysis of Hopfield neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 68-72.

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